Correct. Regarding turning off the center pumps. On a normal flight where you loaded more than 7.6T of fuel, there will be fuel in the center tank so you will most likely use 6 pumps on from preflight until the center tank runs out in flight. The center pumps output more pressure than the wing pumps so with 6 pumps on, only fuel from the center tank will be used until it runs out.
When the center tank gets depleted you will get Master Caution → Fuel and the amber LOW PRESSURE light on the center pumps will illuminate. Then the pilot monitoring will switch off the center pumps (there’s a QRH checklist for this, but we do it by memory). On current airplanes with automatic pump shutoff (PMDG), as soon as this LOW PRESSURE light comes on, the center pumps will automatically stop pumping. This is because these pumps get hot and their only coolant is the fuel itself. A pump running dry is a fire hazard. In older airplanes, where the pumps didn’t have the automatic shutoff function, the AFM states “dryrunning the pumps is prohibited”. Some people were like “let’s run them a little bit longer to suck out those last Kgs”… ridiculous mainly because of the next thing I’m going to write.
Any residual fuel remaining in the center tank (a few tens of Kg) will be automatically transferred to the LEFT tank by the center scavenge jet pump. This is a slow transfer that starts as soon as the wing tanks reach 50% and the main pump No.1 must be on. This is transparent to the pilot. So basically if your total fuel is 3.6 (half wings) and you’ve followed the fuel usage guide, the center tank will be completely dry.